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Theses and Dissertations Thesis Collection

1967-06

The Intertropical Convergence Zone and Vertical

Motions Using A Diagnostic Numerical Model.

Murray, John Francis

Monterey, California. U.S. Naval Postgraduate School

http://hdl.handle.net/10945/12376

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NUMERICAL MODEL

PHIL GEORGE PROKOP

JOHN FRANCIS MURRAY

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THE INTERTROPICAL CONVERGENCE ZONE AND VERTICAL MOTIONS

USING A DIAGNOSTIC NUMERICAL MODEL

by

Phil George J^rokopLieutenant Commander, United States Navy

B.A., San Diego State College, 195^

and

John Francis MurrayLieutenant, United States Navy

B.A., Villanova University, 1959

Submitted in partial fulfillment of therequirements for the degree of

MASTER OF SCIENCE IN METEOROLOGY

from the

NAVAL POSTGRADUATE SCHOOLJune 1967

D HfUit^C #

ABSTRACT

A diagnostic, non-linear "balanced model is applied to a

case study in the tropical Western Pacific on 1 and 3 March

I965. The region includes both sides of the equator and

contains the ITCZ.

A discussion of the ITCZ is given and the model is dis-

cussed along with the processing of the input data. The study

contains the horizontal wind velocity and the thermal dis-

tribution as input values. The non-divergent stream function

(f) is obtained by relaxatA&n of »Hhe Poisson Equation, V ^ =

|fc.V*V»3 , where the vorticity is computed from the observed

wind field. A comparison is made between the non-divergent

part of the wind and the actual wind. Computer analyzed

stream functions at several levels are shown and discussed.

Dry adiabatic vertical velocities are obtained and com-

pared with the ITCZ. Typical magnitudes are on the order of

0.5 cm/sec. The forcing functions of the co equation are

shown and the contributions, in partitioned form, by various

terms are illustrated and discussed at several levels.

DUDLEY KNOX LIBRARYN." oRADUAT SCHOOLMONifcrxi. CA 9394o-o101

ERRATA

Title Page: Chairman, Department of Meteorology add and Oceanography

p. 2k, par. 2, line 8 change effects to affects

p. 27, par 2 l), line 1 change spare e .to sparse

P- 75 >paragraph "beginning Verticle structure , line 7 change overlaid to

overlain

TABLE OF CONTENTS

CHAPTER PAGE

I. INTRODUCTION 11

II. DESCRIPTION OF THE MODEL 17

III. RESEARCH PROCEDURES AND PROBLEMS 25

IV. CASE STUDIES 31

0000Z 1 March 1965 31

0000Z 3 March 1965 ^9

V. CONCLUSIONS AND RECOMMENDATIONS FOR

FURTHER STUDY 79

VI. BIBLIOGRAPHY 82

LIST OF ILLUSTRATIONS

FIGURE PAGE

1. Mean positions of the equatorial trough inthe IGY months of August S7 and February 58and over Southeast Asia in early May. 14

2. Locations of the radiosonde and pibal sta-tions used in the data analysis. 26

3. Surface pressure, 00Z 1 March 1965. 32

4. Nephanalysis, 1 March 1965

.

33

5. Streamlines and isotachs at 1000 mbs

,

00Z 1 March 1965. 35

6. Streamlines and isotachs at 850 mbs,00Z 1 March I965. 35

7. Streamlines and isotachs at 700 mbs,00Z 1 March 1965. 36




11. Temperature analysis at 850 mbs,00Z 1 March 1965. 38

12. Temperature analysis at 200 mbs,00Z 1 March I965. 38

13a. Vertical cross-section of temperaturedeparture ( °C ) from horizontal meanrelative to equatorial trough - ocean

13b. Vertical cross-section of departure ofheight of isobaric surfaces (tens of feet)from horizontal means.

40

40

14. Geopotential height at 1000 mbs,00Z 1 March 1965. ^

15- Absolute vorticity at 1000 mbs,00Z 1 March 1965. ^1

FIGURE

16.

17.

18.

19.

20.

PAGE

Non-divergent stream function at 800 mbs,00Z 1 March 1965. ^3

Non-divergent stream function at 200 mbs,00Z 1 March 1965. ^3

A comparison of the input and the non-divergent wind values. kk

Total vertical velocity at 900 mbs,00Z 1 March 1965. ^5

Total vertical velocity at 700 mbs,00Z 1 March 1965. ^5

21. Total vertical velocity at 500 mbs,00Z 1 March 1965. ^6

22. Total vertical velocity at 300 mbs,00Z 1 March 1965. ^6

23. Vertical variation of CO. ^8

2k, Nephanalysis for 0251Z 3 March 1965. 50

25. Surface pressure, 00Z 3 March 1965. 51




29. Streamlines and isotachs at 500 mbs,00Z 3 March 1965. 5^

30. Streamlines and isotachs at 300 mbs,00Z 3 March 1965. 5^


32. Temperature at 900 mbs, 00Z 3 March 1965. 57

33. Temperature at 500 mbs, 00Z 3 March 1965. 57

3k. Temperature at 300 mbs, 00Z 3 March 1965. 58

FIGURE PAGE

35. Geopotential height at 1000 mbs,00Z 3 March 1965. 58



38. Geopotential height at 400 mbs,O0Z 3 March 1965. 6o

39' Geopotential height at 200 mbs,00Z 3 March 1965. 6o

40. Static stability at 1000 mbs,00Z 3 March I96.5. 62

41

.

Static stability at 300 mbs,00Z 3 March 1965. 62

42. Absolute vorticity at 1000 mbs,00Z 3 March 1965. 6k

43. Non-divergent stream function at 1000 mbs,00Z 3 March 1965. 64

44. Non-divergent stream function at 800 mbs,00Z 3 March I965. 65




48. North-south cross-section of actual windspeed versus zonal non-divergent componentat 140° E, 200 mbs, 00Z 3 March 1965. 6 8

49. Total vertical velocity at 900 mbs,00Z 3 March 1965. 69

50. Total vertical velocity at 700 mbs,00Z 3 March 1965. 6^


FIGURE PAGE


53. Relative vorticity (for computation offriction) at 1000 mbs, 00Z 3 March 1965. 73

5^. Frictional component of the verticalmotion at 900 mbs, 00Z 3 March 1965. 73

55« Vertical velocity component due to thedifferential vorticity advection by thenon-divergent part of the wind at 700 mbs,00Z 3 March 1965. 7&

56. Vertical velocity component due to theLaplacian of thermal advection by the non-divergent part of the wind at 700 mbs,00Z 3 March 1965. 7&

57* Net contribution of vertical velocity fromeight forcing functions after subtractingvorticity advection and Laplacian of thermaladvection components from the total verticalmotion at 700 mbs, 00Z 3 March 1965. 77

58. Pressure versus vertical velocity (W)at 8° N 1^4° E, 00Z 3 March 1965. 78

TABLE OF SYMBOLS AND ABBREVIATIONS

Cp Coefficient of specific heat at constant pressure

T Coriolis parameter

3 Acceleration of gravity

IK Unit vector in the z-direction

P Atmospheric pressure

ft Specific gas constant

0-" Static stability

T Temperature

VH Horizontal velocity vector

E Height of the isobaric surfaces

o< Specific volume

& Northward variation of Coriolis parameter

S Potential temperature

Geopotential , gZ

^( Velocity potential for the irrotational componentof velocity

^ Stream function for the non-divergent componentof velocity

CO The individual change of pressure, dp/dt

V Isobaric gradient operator

V Laplacian operator

\J* Jacobian operator

*4 Zonal component of the wind

V" Meridional component of the wind

Wf Zonal component of the non-divergent wind

V^ Meridional component of the non-divergent wind

3 Relative Vorticity

5,.

?

cB

H s

Hl

mb

ITCZ

neph

prog

TI

1

Absolute vorticity

Density

Drag coefficient

Sensible heating function

Latent heating function

Millibar

Intertropical Convergence Zone

Nephanalysis

Prognosis

RTP©

C f M."Vul +Vl

*fy c J>>r,

Vur+v3

10

I. INTRODUCTION

The tropical atmosphere has "been the object of an in-

tensive research effort in recent years. No single, dynam-

ically consistant model has been developed which yields com-

pletely acceptable results, and although great progress has

been made through computer application to case studies, some

of the questions raised are still unanswered.

Lack of conventional data severly hinders analysis in

any tropical study and it seems unlikely that a significant

improvement in the number of reporting stations is forth-

coming in the near future. The alternative for those in-

terested in the problem is to rely more heavily on "uncon-

ventional" or satellite data, including photographs and

radiation data, and possibly satellite tracking of constant

level balloons. The Intertropical Convergence Zone(ITCZ)

the Equatorial Trough, and the Intertropical Front have

been used by various meteorologists to describe the same

meteorological phenomena. A finer distinction could per-

haps be made, but for the purpose of this paper ITCZ is

preferred and will be defined as a relatively narrow,

quasi-continuous band of convective clouds encircling the

earth with associated synoptic scale vertical velocities

caused by the convergence of air masses originating in the

Trade Wind systems of both hemispheres. The other defini-

tions will be used interchangeably when referring to the

literature. The weather associated with this zone is often

severe, convective in nature, and in the tropics exceeded

only by hurricanes and typhoons.

11

A multi-level diagnostic non-linear balanced model

is a useful tool in studying the three-dimensional struc-

ture of the atmosphere and such a model has been success-

fully used by Krishnamurti (1966) in tropical and mid-

latitude studies. Charney (1963) argued that vertical

motions in the tropics are small and may be neglected.

Krishnamurti believes that even though small, they may

play an important role in the dynamics of the tropics.

He found typical values of vertical velocity on the

order of 0.1 cm sec in a typical Carribbean easterly

_iwave and 1-2 cm sec in the considerably more active

Indian monsoon circulation which becomes part of the

ITCZ during the northern summer. Together with the

horizontal winds, the vertical velocity completely

describes the three-dimensional motion of the atmos-

phere.

The authors applied the model used by Krishnamurti

and Baumhefner, (1966) with some modifications, to a

case study in the Western Pacific in order to obtain

vertical velocities in the ITCZ. Other considerations

motivating the work were, to investigate the non-diver-

gent stream function derived from the relative vorticity

field on and near the Equator, and to define initial

state conditions for use in a more sophisticated model,

such as a primitive equation prediction scheme as sug-

gested by Charney, (1962),

A barotropic model is currently being used to fore-

cast the non-divergent wind field and at present is pro-

12

ducing acceptable results. Once the data problem in the

tropics is solved, however, the baroclinic terms will

have to be included and a significant improvement should be

realized.

History . Historically the ITCZ has been a frustrating

and confusing phenomenon. Lacking a complete understanding

of the major forces involved in the tropics, meteorologists

of various schools attempted to apply their theories to the

tropical problem. Palmer (1951) and Riehl (195^) divide the

approaches into three broad categories: Climatclogical

,

Air Mass, and Perturbation. The Climatologists based their

interpretation of the ITCZ on long term mean charts, statis-

tical in nature, and based on a simple general circulation

theory. The data network in the tropics may be sufficient

for their purposes, however, they are unable to explain the

large daily fluctuations and severe storms frequently found

in the equatorial regions. The mean position of the equa-

torial trough, based on isobar ic analysis, is shown in

Fig. 1. The Scandinavians, who are primarily responsible

for the air mass approach, applied their frontal theory to

the tropics and the term Intertropical Front was coined.

Indeed, the weather was of a frontal nature caused by the

air masses of the two hemispheres converging in a low

pressure trough, although a significant density discon-

tinuity was not observed. The ITCZ was subsequently de-

scribed by various authors as:

13

c03

o-*A

pto

3to3<:

o

wx:-p

co

fHCJ •

H >»CO

<D g-P >»

t-{

C ^•H CO

CD

s:to c

ofc CO-p *-l

CO

H <J00

•H -P*H CO

O CO-P CD

CO -C3 -PC? 3M o

CD

P CD

<m Oo

•xi

co cC CO

o

-P xo

w >>O *H

ft co

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CO CD

55fr

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14

1) a single and continous front

2

)

a double front

3) part single and part double fronts

k) discontinuous

5) sloping toward the summer hemisphere

6) sloping arbitrarily

7) not sloping at all

8) it moves discontinuously

9) it disappears at one location while

another forms at a new location.

It is not surprising that this theory also failed the test

in that it could not be used as a short term forecast aid.

No dynamic explanation could be offered for the varied

structure and movement of the front and the theory was

abandoned.

Riehl (195^0 describes Palmer's attempt to consol-

idate the previous work into a unified picture in the

Perturbation approach theory. In a Pacific study he

found that the East Central Pacific wind constancy is

high and the equatorial trough has little variation.

Small disturbances that perturb the flow are either

brought into the area or develop there. They then move

downstream as waves in the Equatorial Easterlies. Con-

vergence in the basic flow tends to amplify cyclonic

crests and dampen antlcyclonic ones. If the axis of

symmetry for the waves is on the equator, both northern

and southern crests of the waves represent cyclonic

15

circulation and will intensify due to the convergent

flow. This may lead to what has been termed a split or

double equatorial trough. With continued amplification,

closed circulations appear and a west wind finally appears

at the equator. The result of a large number of these

circulations near the equator becomes evident in a mean

wind analysis showing a west component in very low lati-

tudes. These west winds are shown by Wiederanders (1961)

to appear only below 500 mbs. Originating in the trades,

they cross the equator, recurve and form a westerly

asymptote of convergence. This phenomena seems apparent

in this study on 1 March.

The Perturbation approach, although a significant

improvement over the Climatological and Frontal approach,

was not wholly satisfactory and many of the dynamic prob-

lems are still with us.

16

II. DESCRIPTION OF THE MODEL

Dynamical multi-level models enable a study of ver-

tical motions of a particular system or area. The concept

of using balanced models for providing an initial state

for primitive equation models was first proposed by

Charney (1955) • The balanced model initial state has the

advantage of suppressing the unwanted gravitational in-

stabilities that observed initial data might generate.

In recent studies of tropical storms, balanced models

have been proposed by Ooyama (1963). Charney (1963),

Rosenthal (1964) and Kuo (1965).

A multi-level diagnostic balance model has been

demonstrated to be a powerful tool for studying the

three-dimensional details of the non-geostrophic be-

havior of the atmosphere during various stages of a

storm development (Krishnamurti , Nogues and Baumhefner,

1966). Baumhefner (1966) used a similar model, but with

additional terms, for a case study in the Caribbean.

The model presented here is essentially the same as that

used by Baumhefner, but with minor modifications in cal-

culating the non-divergent stream function and using

actual observed temperatures, as suggested by him.

It must be kept in mind that there is actually a

two-fold purpose involved with the use of this model.

One is diagnostic, and the second, and more far reaching,

is that these results are to be used in the future in a

multi-level primitive equation prediction scheme as input

data.

17

The balance model provides a synoptic scale vertical

motion field which is determined by numerical calculation on

a horizontal mesh whose size is a few degrees of latitude.

The numerical model selected to describe the three-dimensional

structure of the tropics is commonly called the non-linear,

or multi-level balanced model (Charney, 1962). Baroclinic

vertical motions of a complete balanced model can be parti-

tioned to determine the unique contributions of several for-

cing functions. These may be looked on as several synoptic

mechanisms producing ascending or descending motions.

A formal derivation of this model has been done by

Baumhefner (1966), and further explanations are contained in

Krishnamurti (1966b). Therefore, this work will not be re-

peated here, other than to give the final form of the omega

equation of a general balance model and to point out the al-

ternate method that was used to calculate the non-divergent

stream function.

The 6j -equation of a general balanced model is expressed

by the following three equations for do , *X , and |^ .

vV^+f^i- f Jp J OvA) + -n V* J (*,•)

-2fefpT(g$)-f>p (lVaX)

-ivX + fi^v^J

-TTv2{-7X-ve?-/3i£ij H (1)

V X S *P (2)

18

+ vx-vs„. + s.vx

These equations are solved by numerical techniques.

The general balance ^-equation, presented here, has

12 forcing functions.

The forcing functions are:

1. "f *p3" CyS* ) Differential vorticity advection by the

non-divergent part of the wind.

2. TI V 3"(^)$) Laplacian of thermal advection by the

non-divergent part of the wind.

3« ""2«>t 5pj'^>, Sy) Differential deformation effect.

4.—fJj,(5V 'Xj Differential divergence effects of a

balance model.

Effects of frictional stresses.5. f *p3apUx "5jJ

c p pEffects of latent heat.

7.—',T"o

" s Effects of sensible heat transfer from

water surfaces to the atmosphere.

8. TXp|^°*p"^J Differential vertical advection of

vorticity.

9. "f dp?^^ '^*pi

Differential turning of vortex tubes.

10. —i ip / * * '

V S^j Differential advection of vorticity by

the divergent part of the wind.

11. ~TI V "W^'VQj Laplacian of thermal advection by the

divergent part of the wind.

19

12. """^Sp 33 "jr Contributipn by the beta term of the

vorticity equation.

It should be noted here that, in this form, none of the

terms "blow up" at the equator where the Coriolis parameter

(f) goes to zero. Instead, the forcing function just drops

out. Zero values are not found in the output, however, due

to the form of the relaxation process.

Calculations of the input values to solve our equations

are, for the most part, pretty straightforward. Five point

schemes are used for the Laplacian, the Liebmann forward ex-

trapolation technique of relaxation is used, Jacobians are of

the standard form and all derivatives are evaluated over dis-

tances 2 Ax and 2£y. The following equations are pertinent.

__. / lCOa \ jfC aPotential temperature: Q - T ( a )

" wDry static stability: (T= ""

p"S ^p (5)

Absolute vorticity:

pe *p

3o,= 77 " sj + 1 (6)

Since an analysis of the geopotential height field is

not easily possible in the tropics, the so-called balance

equation (7), which is a simplification of the divergence

equation, was not used.

v-fVH>= v24>-2j(!£ M)

(7)

If the balance equation is used, the procedure is to

find the non-divergent stream function ( ^ ) from the geo-

potential height. The stream function is then used to find

the vorticity.

20

The procedure was reversed, somewhat, in this paper.

The method used to compute the non-divergent stream function

is the procedure suggested by Thompson (1961), which begins

with a field of isotachs and isogons. The Helmholtz

equation is manipulated to form the equation:

S-(»-$)-V> (8)

By relaxing the field of the vorticity for suitable boun-

dary conditions, the non-divergent stream function on an

isobaric surface is obtained.

The numerical method and boundary conditions for

solving this equation are those given by Hawkins and

Rosenthal (1965). The boundary values of the non-divergent

stream function are made a function of the divergence of

the wind, instead of the zero condition imposed on the

solution by the balance equation. The values depend on

the derivative of the velocity potential (§«) (r\ normal to

the boundary, increasing outward). The boundary values of

22L needed are calculated from an initial "Y-f ield obtained

from the solution of

V X=V*V; %- O on the boundary (9)

where V*V is the divergence calculated from the wind

analysis

.

The non-divergent stream function calculated by this

method is what Baumhefner (1966) calls the kinematic stream

function, and is the method that he felt was most accurate

in the tropics.

21

The numerical model accepts data at five levels (1000,

800, 600, 400, and 200 mbs.) and utilizes the X, Y, P co-

ordinate system. The basic inputs are, the observed tem-

peratures, and the isogons and isotachs of the actual

wind at each level. The basic grid consists of 33 x 15 x 5

points along the zonal, meridional and vertical directions.

Actual grid values are inscribed at 2? grid points in the

zonal direction, but an artificial cyclical continuity is

provided by extending the grid over 6 extra points by fit-

ting a polynomial through the boundary conditions. This

region is a numerical waste-box in the diagnostic studies

but will become essential in the future prediction phase.

A vertical staggering of the grid was used as recom-

mended by Krishnamurti (1966a), and the values of % "% and

-5 appear at 1000, 800, 600, 400 and 200 mbs while ©,T.

<T}co, and|^!£ appear at 900, 700, 500, and 300 mbs. Other

boundary conditions are, o>»7 = dpj^

)

rO at the northern and

southern wall. Boundaries are eliminated in the zonal

direction by the use of the 6 additional points. 60 is taken

to be zero at the surface and at the top of our atmosphere,

100 mbs.

The wind velocity is used to obtain the vorticity, and,

from the vorticity, the stream function is derived. The

static stability is calculated from the temperature. These

terms, together with a frictional effect from the stream-

lines, will yield the first approximation of the vertical

motion.

22

The omega equation, used for the first approximation, does

not contain any terms that are a function of omega. The

first guess of the vertical motion is then used to calculate

the non-linear terms containing omega. The latent heat term

is added at this point, since it is non-linear in nature.

An iterative process is performed until the difference be-

tween successive approximations is considered small.

A brief recapitulation of the general form and effect

of the main forcing functions is warranted. A complete

discussion of all terms is included in Krishnamurti

,

Nogues, and Baumhefner (1966) and Krishnamurti (1966b).

Basically, if the forcing function, F. , is greater

than zero, then in that region we can expect rising motions.

There are exceptions to this rule, but generally this is true

Near the centers of maximum rising or sinking motions, F.

and CO. have been found to be inversely proportional to

each other (Krishnamurti, Nogues, and Baumhefner, 1966).

Baumhefner (1966) has shown that the four main contri-

buting forcing functions in the tropics are terms 1, 2, 5»

and 6 (page 19). The first two terms are the simplest to

interpret. The effect of differential vorticity advection

(term 1) is that if in the upper air there is a region of

strong positive vorticity advection by the non-divergent

component of the wind, then F. is greater than zero and

rising motions would be found. The inverse holds for

sinking motions. The Laplacian of thermal advection

(term 2) has the effect, that at centers where warm air

23

advection is a maximum by the non-divergent component of

the wind, F„ is greater than zero and again rising motions

will be found. The inverse again holds.

The other two terms, friction and latent heat, are of

great significance in the tropics and are explained in

great detail by both Krishnamurti (1966b) and Baumhefner

(1966). Generally, F^ (friction) will contribute rising

motions in regions of cyclonic relative vorticity and sink-

ing motions in regions of anticyclonic relative vorticity.

This effect will only be felt significantly at the 900 mb

output level. A drag coefficient (C-J of 2.0 x 10 J was

used, and held constant in the horizontal.

The latent heat term (term 5) contributes in the tro-

pics where the following conditions are met:

1. The atmosphere is conditionally unstable.

2. Net moisture convergence in vertical columns is

greater than zero.

3. The relative humidity at the particular level is

greater than or equal to 60 percent.

This term only effects levels above 900 mbs, as that level

is used as the top of the boundary layer. It is apparent

that the latent heat term will have its greatest contribu-

tion to the rising motions where cumulus clouds are present

2k

Ill* RESEARCH PROCEDURES AND PROBLEMS

Initially, an attempt was made to produce a compre-

hensive, five day analysis covering the major portion of

the Pacific from ^0°N to ^0°S. Plotted, mercator,

1:^0,000,000 charts were obtained from the Hawaii

Institute of Geophysics, University of Hawaii for 1

through 5 March 1965- Map time is 00Z. This period

was chosen to allow a comparison of our results with

those of Smagorinsky, whose report will be published at

a later date. Since hand analysis had to be employed to

prepare the input data, time considerations became a

limiting factor and case studies on 1 and 3 March were

agreed upon. The model employed in this study contains

27 grid points in the zonal direction and 15 points in the

meridional direction spaced 2 degrees apart. This grid

was placed in the area of most dense data in the Western

Pacific where the analysis was felt to be most reliable

and a well defined, if rather large, ITCZ was observed

on the nephanalysis. The grid is bounded by the 128 E

and 180° meridians and the l4-°N and Ik S parallels.

The area includes approximately 5.1 million square miles

and contains sixteen reporting stations (Fig. 2 ).

Eleven of these are Radiosonde stations and 5 are Pibal

stations, which report upper winds only.

Streamline, isotach, and temperature analyses were

prepared for the 1000, 850, 700, 500, 300, and 200 mb

levels, as well as a surface pressure analysis.

25

CO

CO

>»

2 i-H

CO

# cCO

§ CO

.p

6CO

O)

,c

in-p

D c*-<

* Ti

2CD

CO

3

r CO

co* T-l

\ p«£ coi^ -p

©CO

HCO

£>f-i

AnBCO

1CO

TJp

hoCO

< o

t CO

* u

CO

JZ

-1-p

c o

CO

0.co

•r-t

+J

• CO

ooa

•

CO

bO.Hfe

26

Isogon values were extrapolated to grid points using

a parallel motion protractor and tabulated to 1 degree

accuracy. Isotachs were analyzed at 5 knot intervals and

extrapolated to tenths of knots. Temperatures were ana-

lyzed to whole degrees Centigrade and tabulated to

tenths of degrees at grid points. Surface pressures were

analyzed at one millibar intervals and tabulated to tenths

of millibars.

A preliminary moisture analysis was prepared but was

not satisfactory for our purposes and is not included in

this study. The reason for its omission was based on two

considerations

;

1) The data was too sparce, and unreliable

values were felt to have been generated

at grid points between reporting stations.

2) The nephanalysis revealed only the gross

features of the moisture field. A subjec-

tive scheme was considered, whereby typical

relative humidities would be assigned to

cloudy areas, and the moisture constructed

from the humidities, however, lacking ac-

tual cloud photographs this method was also

considered likely to result in inadequate

gradients in both the horizontal and vertical

The omission is a deficiency of this study since the

release of latent heat is a major contributor to the ver-

tical velocities in the tropics. The influence of terrain

is also neglected.

27

Large vertical velocities can be obtained through orograph-

ic triggering mechanisms which would otherwise be unex-

plained dynamically.

Tiros IX negatives were obtained from NWRF Ashville,

for the period 1 through 5 March 19^5 » but no useable

frames were observed covering the area of interest during

the days analyzed. Nephanalyses were constructed from

the Tiros IX catalog, and original facsimile nephs

,

scaled to the computer output grid size. Channel two,

8-12 microns, Radiation Data was obtained from Goddard

Space flight Center and was analyzed for March 3rd.

A minimum amount of subjectivity was employed in each

of the analyses. The nephs were used as an aid in sparce

data areas to locate major centers or regions of conver-

gence. Wiederanders ' Analysis of Monthly Mean Resultant

Winds over the Pacific was also employed as a consistancy

check. No reports were eliminated and gradients were

extrapolated linearly in all fields. A few aircraft re-

ports at non-standard levels were available and used if

they could be extrapolated to the standard level without

significantly altering the basic analysis. Vertical space

or time cross-sections to eliminate or smooth erroneous

data were not constructed due to time and data limitations.

The observed height fields were not analyzed for in-

clusion in this report in a smooth form. Rough sketches of

these were prepared by the authors to compare with the geo-

potential heights constructed by the computer, on the basis

28

of input temperatures. The geopotential surfaces did not

agree well with either the observed heights or the winds.

Moreover, a continuous degradation was noted with increas-

ing height. Baumhefner attempted to correct this in his

study by subjectively modifying the geopotential heights

to fit the observed winds, although weak temperature

gradients may have been altered significantly. He remark-

ed that using the observed, unadjusted geopotential heights

to calculate thickness may lead to a more reliable calcul-

ation of temperatures. The authors, however, did not

attempt this experiment, although it appears worthy of

investigation.

To insure a smooth vertical temperature structure,

successive averaging was accomplished, which resulted in

the output temperatures varying slightly from input values.

Since the machine accepts data at the even levels men-

tioned previously, several techniques were employed to

convert the data at the standard levels to the input

levels within the computer. All data at the surface and

200 mb levels were used without modification. The tem-

perature at 850 mbs was reduced to the 800 mb value, using

a tropical, standard atmosphere lapse rate. The 600 and

^-00 mb levels were obtained using the mean of the 700 -

500 and 500-300 mb levels, respectively. The same scheme

was used for wind data except that the wind vectors were

separated into u and v components prior to averaging. The

850 mb winds were used directly as the 800 mb values.

29

A vertical staggering of the grid is convenient due to

the nature of the hydrostatic and «o equations. The first

part of the program, which does not include vertical veloci-

ties, yields outputs consisting of, temperature, potential

temperature and static stability at the 900, 700, 500, and

300 mb levels. Geopotential heights, the stream function,

and absolute vorticity appear at the 1000, 800, 600, ^00,

and 200 mb levels. The cj portion of the program provides

vertical velocities at the 900, 700, 500, and 300 mb levels

and we assume *> = at the surface and 100 mbs which repre-

sents the top of our atmosphere. The contributions to the

total t*i by various forcing functions are obtained, which

allow an examination of their effects in the tropics. The

sensible heat term contributed nothing in this study since

we assumed thermal equilibrium between the atmosphere and

ocean in the tropics. A discussion of the output charts

is made in Chapter IV. The program was solved on an IBM

709^ computer and takes approximately one hour per case

study.

30

IV. CASE STULIES

OOOOZ 1 MARCH 1965

Synoptic situation . The most significant features in

the surface pressure pattern on 1 March 1965. (Fig. 3). are

the low pressure center located in North Central Australia,

and the trough extending from the Southern Hemisphere mid-

latitudes to the equator. Two small high pressure centers

are located in the Southern Hemisphere, one over New Guinea,

and a second at 180 longitude. A secondary zonal trough is

evident at 4°N extending from 1^5 E to 180 . The surface

streamline pattern (Fig. 5) agrees well with the pressure

field. The winds are cyclonic around the Australian low

with strong cyclonic shear and curvature, and the winds are

anticyclonic around the high centered at 180 . The trough,

which has been labeled Frontal on the nephanalysis , does

not show up clearly in the wind field, but this is an area

of very light winds and only a few reports were available.

An asymptote of convergence is located in the zonal trough

in the Northern Hemisphere. The winds to the north are

extremely steady in direction but strong anticyclonic shear

exists north of the isotach maximum at 6 N 164- E. A cy-

clonic eddy exists at 148 E just north of the equator.

Equatorial Westerlies are formed as the N.E. Trades cross

the equator and recurve west of 150 E under the influence

of a change in sign of the Coriolis force. A split ITCZ

forms. The nephanalysis (Fig.^-) depicts, in the eastern

section (orbit k^>6) , the clouds associated with the frontal

31

s:ouCO

(XIoo

U

CO

CO

<r>

Uft

CO

oCO

CO

to

fX4

32

£J O 00 (O

33

trough, an open area to the east and an ITC band located in

the Northern Hemisphere in the area occupied by the zonal

trough. The TTCZ is displaced far north of its mean posi-

tion, which is at 8 South in February and early March. The

western portion of the neph, orbits ^57 and ^58, shows most

of the entire grid covered by clouds. The mostly open area,

less than 5/10 coverage, in the northwest corner, is the

result of a small high pressure ridge extending southward

from higher latitudes. The ITCZ is an extremely wide band

and is split into a northern and southern part. The south-

ern band is not easily explained by the pressure field and

we suspect a large terrain influence in this region. The

850 and 700 mb flow patterns (Fig. 6,7) are similar in most

respects to the surface. At 500 nibs (Fig. 9) the eddy which

appeared north of the equator disappears and a large conver-

gence area is found at 1^-0 E 7 North. The Australian cyc-

lone is still evident but the influence of the subtropical

high pressure belts is becoming more apparent. At 300 and

200 mbs (Figs. 9, 10) these belts are the dominating features.

More variability is noted at 200 mbs than at 300 mbs.

The observed temperature structure is very complex and

appears to have little vertical continuity. Strong grad-

ients may exist in localized areas which were not picked up

in the analysis. The 850 and 200 mb temperatures are shown

(Figs. 11,12) and they clearly show a reversal in the temper-

ature gradient in the vicinity of the ITCZ. This feature was

discovered by Schnapauff in the Atlantic and verified by

3^

130E

10 N

10 S

Fig. 5. Streamlines and isotachs at 1000 mbs, 00Z 1 March1965. Isotach interval, 5 knots.

ION

10 s

Fig. 6. Streamlines and isotachs at #50 mbs, 00Z 1 March1965. Isotach interval, 5 knots.

35

10 N

10 S


10 N

10S


36

180

10 N

10 S


10 N

10S


37

130E

10 N

10 S

Fig. 11. Temperature analysis at 850 mbs, 00Z 1 March 1965,Temp, in degrees Centigrade. Isotherm interval,1 degree.

130E 140 150 160 17C 180

S* -ff» -««*

10 N

10S

Fig. 12. Temperature analysis at 200 mbs, 00Z 1 March 1965Temp, in degrees Centigrade. Isotherm interval,1 degree.

38

Simpson in the Pacific. Riehl( 19.58 ) prepared a vertical

cross-section of the typical temperature in the region of

the equatorial trough, which is included for comparison

(Fig. 13a). Riehl also prepared a vertical cross-section

of heights for this region (Fig„13'b), and a comparison

may be made with geopotential heights computed in the pro-

gram from the surface pressure and vertical temperature

structure. The 1000 mb geopotential height field (Fig.l^)

is shown as an example.

An example of the absolute vorticity, computed from

the observed wind field, is shown for the 1000 mb level

(Fig. 15).

39

Fig. 13a.tot ilutfc rciotivc tquot. trough

Vertical cross-section of temperature departureI c; from horizontal mean, relative to equatori-al trough, ocean a-t^ao

8

Lotitudt retOlivt CQuot. troughPig 13b. Vertical cross-section of departure of height ofisobaric surfaces (tens of feet) from horizontalmeans.

^0

. I28E14 N

160

H 1 f jjf176

H h

Fig. H*. Geopotential height at 1000 mbs, 00Z 1 March 1965.Heights in meters. Interval, 10 meters.

. 128 EI4N-.

U2 136 140 144 148 152 156 160

Fig. 15. Absolute vorticlty at 1000 mbs, 00Z 1 March 1965,Interval 10 x 10"b sec" 1

.

kl

Results . The results obtained through the application

of this model to our study are most encouraging, particu-

larly in the Northern Hemisphere where better data cover-

age was available. The stream functions generated through

the relaxation of the vorticity field at 800 and 200 mbs

are shown for 1 March in Figures 16 and 17 . A comparison

was made of the non-divergent wind and the actual winds in

a meridional cross-section. At 800 mbs, only the u. com-

ponent of the actual wind is used since the cross section

passed through the circulation center at 1^8 E, and the

directions were more variable at this level. At 200 mbs,

the longitude was chosen so that the streamlines had

their maximum zonal values, and here, the total isotach

value was used. These are plotted against the zonal

stream wind U.^ and are shown in Figure 18.

Baumhefner (1966) found that the non-divergent part

of the wind was about ^0% of the total wind and his results

are clearly verified. Stream functions at the other levels

yielded similar results.

Dry adiabatic vertical velocities are shown at the

900, 700, 500, and 300 mb levels , (Fig. 19-22 ) . An ITCZ

was drawn in the areas of maximum rising motion on these

charts such that it remained within the boundaries of the

ITCZ indicated on the nephanalysis and at the same time

was vertically consistent. The Northern Hemisphere fit

was remarkable.

hz

Fig. 16. Non-divergent stream function at 800 mbs,?

00Z 1 March 1965. Isoline interval, 10x10-5 msec .

14 N

I4S

Fig. 17. Non-divergent stream function at 200 mbs,? 1

00Z 1 March 1965. Isoline interval, 1 0x1 0"5 msec" .

43

12A

» .^ /

8

s4 f ^*\^

°N

^^ • -/sycu» / ys

( ( - M »

4 iu*)

8

12

—

20 10 W E 10(Knots)

144 E 800mb

20 30

Fig. 18. A comparison of the input and non-divergent windvalues.

M

Fig. 19. Total vertical velocity at 900 mbs, 00Z 1 March1965. Arrows indicate direction. Interval is10xl0~-5 mbs sec~l.

tarffe 132 136 140 144 148 152 156 160 164 168 \1

Fig. 20. Same as above except 700 mbs.

^5

. 128 E 132 136 ,4<_ 144 i48 152 156 160 164 l«

H—I—

h

172 176

H—h- 180

tjH—t-H—i—i—i—^—i—i—i—'—b—i

—

t-'—i—i—i—»—i—i—i—i

i i—jta2ffE 132 136 140 144 148 152 156 160 164 168 172 176 ,8°

Fig. 21. Total vertical velocity at 500 mbs , 00Z 1 March1965. ^Arrows indicate direction, interval islOxlO"-5 mbs sec"" 1

.

I28"E 132 136 WO 14a 148 152 156 160

Fig. 22. Same as above except 300 mbs.

176 180

^6

Two points were chosen in the vicinity of the ITCZ

,

one at l64°E, 4°N in the eastern portion of the neph and

a second at 138 E, 6 N in the western section, and a graph

showing the variation of c*i in the vertical was constructed

(Fig. 23). Typical magnitudes were found on the order of

- 'i -150 to 80 x 10 J mbs sec (rising) in the frictional layer,

-5 -1decreasing to less than 20 x 10 mbs sec above the

frictional layer and with a secondary maximum in the mid

and upper troposphere. This corresponds to Krishnamurti '

s

theory that two maxima exist in the co field in the ver-

tical, the lower caused primarily by the influence of

frictional convergence, which drops off at intermediate

levels, and the second maximum in the mid and higher trop-

osphere, where more closed circulations are found.

^7

JQ

E

3(0(A

0)

I

-80 -60 -40 -20

,U), (I0"

5 mb/sec)Fig. 23. Vertical variation of to.

^8

OOOOZ 3 March 1965

Synoptic situation . By the third of March we find that

the nephanalysis for 0251Z (Fig. 24), from Tiros IX orbits

480-482, indicates that the Intertropical Convergence Zone

is undergoing a major change with the northern section weak-

ening and a second ITCZ intensifying to the south, so that

there are actually two ITC ' s at 00Z on 3 March. The north-

ernmost is defined mostly by the cloud picture and the use

of the water vapor channel two data from Tiros VII indicates

that it is most intense below about 20,000 feet.

The southern ITCZ is well defined by both clouds and

convergence of the wind field with the channel two data in-

dicating it extends to greater than 30,000 feet. Since the

southern ITCZ is better defined by the wind field, much of

the discussion of the streamlines will concern this area.

It is interesting to note that the nephanalyses for

the 1st through the 4th of March show the continuous se-

quence of events of the change in the ITCZ. This phenome-

non has been observed before by Airborne Early Warning

Squadron 4 which made daily flights in the Eastern Pacific

equatorial region for a period of 1§ months in 1957, during

which time it was observed that the ITCZ intermittently

moves rapidly north, dissipates, and reforms in the south

(Roth, 1958).

The surface pressure analysis (Fig. 25) does not show

the change in synoptic situation so dramatically, with the

off season front still trailing down into the tropic region

49

'2 ^ O 00 ID

to

3

<D

CO

CO

r-l

O

CO

Fh

OS

•dccc

-p •

co co

CO

c

\oOvd

£ OO -PFh 00

co s:£ I

CO

r^ co

ots] Ut-H ovr»

CM CO

O CO

*H CO £<iH O

CO CO

T-t

CO <D

>» ui-i co

CO

c co

CO -x: tsi

Q) E-f

S3 M

c\i

to

50

fU* n* if**!

Fig. 25. Surface pressure field, OOZ 3 March 1965Interval, 1 millibar.

rs*t l*K i$»*f \t+* iicrt.

Streamlines and isotachs at 1000 mbs, OOZ 3 March1965. streamlines, isotachs.Isotach interval, 5 knots.

51

with low pressure extending northwest across the equator

and a 1010 mb ridge located over the southern half of New

Guinea. The streamlines and isotachs at the surface

(Fig. 26) also support the pressure analysis, although we

would expect a little more cross-isobar flow near the equa-

tor because of the diminished Coriolis parameter.

It is the authors' opinion that the anticyclonic and

cyclonic eddies to the south and north of New Guinea, re-

spectively, are caused by the effect of the mountainous

terrain of New Guinea on the wind flow. The cyclonic cir-

culation in the north hemisphere has weakened considerably

since the 1st of March when it extended through several

levels. On the 3rd it is only indicated by a slight wave

at 850 mbs (Fig. 27) and disappears completely above that

level. The southern ITCZ is well defined by the 850 mb

streamlines and there is an excellent correlation with the

nephanalysis

.

The streamlines also indicate a reason for the weak-

ening of the northern ITCZ, as divergence is indicated near

the middle of the zone.

As we go upward in the atmosphere (Fig. 28), we can

see that all trace of the cyclonic circulation to the north

has disappeared but that the anticyclonic ridge over the

south of New Guinea intensifies with height (Figs. 29, 30)

and becomes a closed circulation by 300 mbs with outflow

taking place.

We also find that we now have some divergence taking

place over the southern ITCZ. The Subtropical Highs have

52

Fig. 27. Streamlines and isotachs at 850 mbs, 00Z 3 March1 965 • streamlines, isotachs.Isotach interval, 5 knots.

cnr

Fig. 28. Streamlines and isotachs at ?00 mbs, 00Z 3 March1965. streamlines, isotachs.Isotach interval, 5 knots.

53

Fig. 29. Streamlines and lsotachs at 500 mbs, 00Z 3 March1965. streamlines, lsotachs.Isotach interval, 5 knots.

I*S

Fig. 30. Streamlines and isotachs at 300 mbs, 00Z 3 March1965* streamlines, isotachs.Isotach interval, 5 knots.

5^

moved equatorward and they can be seen clearly at 200 mbs

(Fig. 31 ) • The anticyclonic circulation persists at this

level along with the divergence over the northern coast of

New Guinea. There is now some convergence a little to the

north of this area.

By looking at the temperature structure at low, inter-

mediate and high levels (Figs. 32-3^) » we can see the anti-

cyclonic ridge appears cold near the surface and the cyclonic

circulation to the north is warm core. There is a persistent

warm area to the southeast. What might be considered an

anomaly is the fact that the region within ^ ot k degrees

latitude of the equator on both sides appears to be rela-

tively cool at all levels compared to the surrounding area

and this had a great effect on the calculated geopotential

heights. When one notes that this is an area of consider-

able cloudiness and moisture with high evaporation, it is

more explainable (Riehl, 195^) • The temperature at the

levels shown are the smoothed temperatures that were com-

puted in the program and used in subsequent calculations.

Output . Geopotential heights were built up from the

surface pressure and the vertical temperature structure by

the use of the standard atmosphere for the 3rd of March

(Figs. 35-39) • Although the heights are not used in fur-

ther calculations, they were done as a matter of interest

to compare with Riehl' s model (Fig. 13b) (Riehl and Malkus,

1958). The geopotential heights do not indicate the ex-

treme height anomaly that Riehl found at high levels over

55

»«r *r

Fig. 31. Streamlines and isotachs at 200 mbs , 00Z 3 March1965* Streamlines, isotachs.Isotach interval, 5 knots.

56

Fig. 32. Temperature at 900 mbs, OOZ 3 March 1965. Temp,in degrees Kelvin. Isotherm interval, 1 degree.

. 128 E 142

Pig. 33. Temperature at 500 mbs, OOZ 3 March 1965. Temp,in degrees Kelvin. Isotherm interval, 1 degree.

57

I28E ij2• I28E X 136**, iii r

Temperature at 300 mbs , 00Z 3 March 1965in degrees Kelvin. Isotherm interval, 1

feo

Temp,degree,

. 128 E>4N

Fig. 35. Geopotentlal height at 1000 mbs, 00Z 3 March 1965,Heights in meters. Interval, 10 meters.

58

Fig. 36. Geopotential height at 800 mbs, 00Z 3 March 1965.Heights in meters. Interval, 10 meters.

'< '>* IRQ

Fig. 37. Geopotential height at 600 mbs, 00Z 3 March 1965.Heights in meters. Interval, 10 meters.

59

152 156 160 164

Fig. 38. Geopotential height at ^00 mbs, 00Z 3 March 1965.Heights in meters. Interval, 10 meters.

• I28'E iJ2

14 N

Fig. 39. Geopotential height at 200 mbs, 00Z 3 March 1965Heights in meters. Interval, 10 meters.

60

the ITCZ, instead low pressure was found. This is believed

to be caused by the difference in the vertical temperature

of Riehl's model (Fig. 13a) as compared to observed tempera-

tures on 3 March. The warm anomalies up to 200 mbs were

not found.

A comparison of the 200 mb streamlines (Fig. 31) with

the geopotential height at 200 mbs (Fig. 39) shows little

resemblance to one another, which might be an indication

that an observed height analysis, if enough data were avail-

able, would be considerably different from the geopotential

height. This is a further point to be taken into account

when deciding whether to compute the non-divergent stream

function from the geopotential height or alternately from

the observed winds, as has been done here.

Static stability . The dry static stability output at

all levels indicates two main features, which are illustrated

by the values at 900 and 300 mbs (Figs. kO , kl ) . One is

that values are slightly positive everywhere within the

region on the 3^d of March. The second feature indicates

what we might expect in the tropics, that the gradient of

dry static stability is very small. The same situation had

been found on 1 March. The cloud situation indicates that

the moist static stability would be a significant factor

and that much of the area would be conditionally unstable,

leading to large contributions to the upward vertical ve-

locities from the latent heat forcing function. This would

be mostly true in the areas of extensive cumulus cloud

coverage, such as the ITCZ.

61

Fig. 40. Static stability at 1000 mbs, 00Z 3 March 1965.Interval, 10xl0~3 meters 2 mbs" 2 sec-2 .

i£ 136 AC 144 146 152 156 160 M 166 172 176 ia0 .

I I I I I 4 I 1^ 1 I I I I 1 1 I I I I T I I III '1 -T4-N

' Xol

,44 ' ft ' & ' .56 ' .60I I lit (4*5

180

Fig. 41. Static stability at 300 mbs, 00Z 3 March 1965.Interval, 10xlO"3 meters 2 mbs" 2 sec' 2

.

62

Vorticity . An example of the absolute vorticity out-

put using the actual winds is shown at 1000 mbs (Fig. 42).

It must be remembered, that the signs of cyclonic and anti-

cyclonic vorticity are reversed in the Southern Hemisphere

so that negative values indicate cyclonic vorticity south

of the equator. This introduces some confusion, especially

in areas such as the closed - 10 x 10 /sec center at iy8 E

which is situated on the equator. The fact that the center

extends into both hemispheres indicates anticyclonic vor-

ticity in the northern part of the center and cyclonic in

the southern half. This is not a contradiction if we take

a look at the 1000 mb streamline chart (Fig. 26). The

streamlines indicate a clockwise curvature and has a maxi-

mum in the isotachs south of the easterly winds in that

area. Both of these facts lead to just the picture that is

illustrated by the vorticity center. Anticyclonic vorticity

to the north of the equator and cyclonic vorticity to the

south.

The program takes the change of sign into account when

computing vertical velocities from vorticity effects so that

the sign of cj will be correct in both hemispheres.

Stream function . Computed non-divergent stream func-

tions are shown at 1000, 800, 600, 400 and 200 mbs (Figs.

iJ-3-^7) and a comparison with the streamlines at similar

levels (Figs. 26-31) shows a striking similarity. A north-

south cross-section was selected at random to see the actual

correlation on the 3^d as compared to that found on the 1st.

63

I2& LB

Absolute vorticity at 1000 mbs , 00Z 3 MarchInterval, lOx 10""° sec -1

1965

i?»E 13

Fig. ^3. Non-divergent stream function at 1000 mbs,00Z 3 March 1965. Interval, 10xl0"5 meters 2 sec" 1

,

6^

I4'S

Fig. *j4. Non-divergent stream function at 80Q mbs,00Z 3 March 1965. Interval, 10xl0~-> meters 2 sec" 1

Fig. 45. Non-divergent stream function at 600 mbs,00Z 3 March 1965. Interval, 10x10-5 meters 2 sec" 1

.

65

. 128 E 132

14 Ni136 AC 144 146 152 156 160 168 172 176 , R0

Non-divergent stream function at 400 mbs,00Z 3 March 1965. Interval, 10xl0~5 meters 2 sec" 1

,

Fig. 47. Non-divergent stream function at 2Q0 mbs,00Z 3 March 1965. Interval, lOxlO"-5 meters 2 sec

-1

66

The cross-section was taken at 1^-0°E at 200 mbs. The actual

winds were almost strictly zonal in this area so the entire

wind was taken and compared to the zonal non-divergent com-

ponent calculated from Uy = - tt . The results (Fig. ^8)

show a remarkably close correlation, with some apparent op-

posing winds from the divergent component between 3°N and

3 S and between 5 and 9 S. Note that the true winds pass

through a calm area about 8 S (Fig. 31) and change direction

by almost 180 and the non-divergent component shows the

same results. Near the centers of highs and lows we would

expect a larger contribution from the divergent part of the

wind.

Vertical velocity . The total vertical velocity in

units of lO'-Vb/sec is shown at the output levels of 900,

700, 500 and 300 mbs (Figs. ^9-52) with the ITCZ ' s super-

imposed as hatched double lines to observe the correlation,

if any.

It must be remembered that the vertical velocities

shown here do not include sensible heat, which should give

a minor contribution in the tropics, and latent heat, which

has been shown to be a major contributor to the upward ver-

tical velocities in the tropics. We find a fairly good cor-

relation with the cloud cover and the ITCZ ' s at 900 mbs

(Fig. ^9) , with vertical velocities greater than 1 cm/sec

upward and over 1.5 cm/sec downward. Rising vertical mo-

tions are found over 95 percent of the analyzed ITCZ's with

two intense centers in the north and a weaker one to the

67

°M

L

AT

I

TO

DE

14

12

10

8\ I

6•

• ftW

4

S*2

O

1 /

1

4

6

a - 9 mI* —Mlo - •/

+^f— |ut l

/a

H' '

50 20 /0 o /0W £

Knots

ao 3o 4o

Fig. 48. North-South cross-section of actual wind speedversus zonal component of the non-divergent wind at 140° E,200 mbs, 002 3 Mar. 1?65»

68

!28~E 132

Fig. ^9. Total vertical velocity at 900 mbs, 00Z 3 March1965. sinking, neutral, risingITCZ is cross-hatched. Interval, 20x10-5 mbs sec"*

A,'28E . j£ ,'?6 , -y-

,144

, ^ ,152 , 156 160 K* 168 172 176 IB04 N •—I—I—fe-H—I—I—

1

6 NH—IgH—I—I—b— I—I—I—I—»3—I—I—I—I1 h-«fW N

Total vertical velocity at 700 mbs, 00Z 3 March1965. sinking, neutral, — •?— rising.ITCZ is cross-hatched. Interval, 10xl0~-> mbs sec" 1

69

Total vertical velocity at 500 mbs, 00Z 3 March1965. sinking, neutral, — »— rising.ITCZ is cross-hatched. Interval, 10x1

--5 mbs sec -1

. 128 E IJ2 136 40 m 148 152•4N-1 M—

h

H—I

1 n l»

I h—I h156 160 164 168 172 176 ionH—I—I

11 p l j 1 1 1 1

p—IfM'N

Total vertical velocity at 300 mbs, 00Z 3 March1965. sinking, neutral, ----- rising,ITCZ is cross-hatched. Interval, 10xl0~-5 mbs sec" 1

70

south, indicating that the northern ITCZ may be more active

near the surface. The higher levels show a much poorer

correlation with the ITCZ ' s . The 700 mb output (Fig. 50)

does show rising motions over most of the southern ITCZ and

part of the northern one. Maximum vertical velocities are

of the order of .25 cm/sec. The correlation at 500 mbs

(Fig. 51) is even worse except in one portion of the north-

ern ITCZ where motions are as strong as .35 cm/sec, rising.

The correlation at 300 mbs (Fig. 52) seems to be the worst

of all, but the channel two data for the area indicates that

clouds only extend above 30,000 feet in parts of the southern

ITCZ. Vertical velocities are of the order of .6 cm/sec.

The magnitude of the vertical velocities for 3 March at all

levels are considerably less than for the 1st.

Latent heat . The authors feel that the poor correla-

tion with the ITCZ's at levels above 900 mbs is due to the

lack of the latent heat contribution. Baumhefner (1966)

has shown that the contribution from the latent heat forcing

function easily runs as high as .5 cm/sec and could contri-

bute more. These contributions to the upward motion would

be found in areas with moisture convergence, R.H. > G0% and

conditionally unstable conditions. These conditions would

most likely be found in the areas of maximum cumulus cloud

occurence which are right along our ITCZ's. Therefore, we

feel that the addition of the latent heat team will bring

the vertical velocities into a much closer correlation with

the ITCZ's at levels above 900 mbs.

71

Inclusion of moisture for latent heat will be conducted

this summer in a follow up study by Dr. T. N. Krishnamurti.

Friction . The higher correlation of the 900 mb level

is believed to be due in large part to the effects of fric-

tion. Fig. 53 shows the contribution from the friction

forcing function at the 900 mb level and it can be seen that

there is an excellent correlation with the ITCZ's and that

friction is a large contributor to the total vertical mo-

tion, running almost . ^ cm/sec in some areas, which is over

^0 percent of the total velocity. The authors would agree

with Baumhefner that friction must be considered on a par

with the forcing functions of the differential vorticity ad-

vection by the non-divergent wind and the Laplacian of ther-

mal advection by the non-divergent part of the wind as the

major contributors.

It might be mentioned that, initially, problems were

encountered in computing friction at the 900 mb level and

final friction contribution was not calculated until near

the end of the research time period. As an alternative, in

order to find the areas in which friction would have the

most effect, a method to estimate the frictional vertical

velocity at the top of the friction layer was utilized.

This method is discussed by Panofsky (1956) an(i concerns

the relationship of the frictional vertical velocity,

through the Ekman Theory, to Equation (10).

-*

curl "<j

*» =TT&F) (10)

72

. 128 E 32 136 .4>.

'4N-, 1 (—I1 1 h—

h

56 160 166 168 172 176

H 1 1 1 1 1 1 1 1 1 1—I-

il44 4h1 1 1 1 •

1 !g

I1 1

1 I I I

**

148 152 156 160 164 168 172 176

14-S

80I28"E "ifc 136 140

Fig. 53. Frictional component of vertical velocity at 900mbs, 00Z 3 March 1965* sinking, neutral,

rising. ITCZ is cross-hatched. Interval,10xl0~5 mbs sec" 1

.

aftife

Fig. 5^. Relative vorticity (for computation of friction)at 1000 mbs, 00Z 3 March 1965. anticyclonicvorticity, cyclonic vorticity. Interval,5x10 -6 sec -1

73

Here, W"H is the vertical velocity produced by friction

at the top of the friction layer, *fs is the surface stress,

and 5 denotes the average vorticity between the surface and

the top of the friction layer.

Panofsky shows that this can be expressed in the simpler

form

Here, JJ± is the eddy viscosity, £©js is the surface

geostrophic vorticity, and o< is the angle between the sur-

face wind and surface isobars. The quantity yuf^ can also be

eliminated by means of the relation between the height of

the friction layer, H , and M$ . The result is equation

(12).

WU - a, feg. So,s Sin 2* # , (12)

An estimate can be calculated for the frictional ver-

tical velocity by subtracting the Coriolis parameter (f)

from the absolute vorticity to obtain the relative vorticity

(Fig. 5^). This then can be used in Equation (12), along

with a constant angle, ©<» over the ocean.

An example would be

ior S = 30 x IO~ys*cjH * J

K *,* ND «*• r 3°^

^ 3 0.35* C^/sec

A comparison of Fig. 53 with Fig. 5^ shows a high de-

gree of correlation, if one remembers that negative values

of "5 in the Southern Hemisphere represent cyclonic vortici-

ty and we would have rising motions where they are located.

7^

Other terms . Baumhefner (1966) found that in many in-

stances the contributions of the vorticity advection and

the Laplacian of thermal advection were of opposite sign.

The same results were noted here, as illustrated by a com-

parison of the individual partial vertical velocities due

to these forcing functions at 700 mbs (Figs. 55> 5&) •

The fact that the first two forcing functions, men-

tioned above, are generally the only major contributors to

the vertical velocities above 900 mbs, in the absence of

latent heat, is illustrated by a closer look at the ?00 mb

level. Fig. 57 shows the results if the sum of the contri-

butions from vorticity advection and the Laplacian of thermal

advection is subtracted from the total vertical velocity.

It can be seen that the contribution of the sum of the re-

maining eight forcing functions that were calculated is al-

most negligible.

Vertical structure . A point along the northern ITCZ

was selected for the 3^d of March, as was done for the 1st,

to check the vertical structure of the magnitudes of the

vertical velocities. The results at 8 N 1^4 E are shown in

Fig. 58 and show the same basic structure as on the 1st.

There are large values near the surface, due to friction,

overlaid by small values at 700 mbs and larger values at

higher levels before dropping off to zero at the top of the

atmosphere

.

75

148 IS2 196 160 164 168 172 176 ,80

Fig. 55* Vertical velocity component due to differentialvorticity advection by the non-divergent part ofthe wind, 700 mbs, 00Z 3 March 1965. sinking,

neutral. Interval, 10xl0~5 mbs sec" 1.

Fig. 56. Vertical velocity component due to the Laplacianof thermal advection by the non-divergent part ofthe wind, 700 mbs, 00Z 3 March 1965. sinking,

neutral, rising. Interval, 10xl0"-5 mbssec

-1

76

• I28E 152 136 140 144 148 152 156 160 164 168I4N-

I I I

12..

10..

8..

6..

4..

+H—

h

I . I I—

H

H 1—

h

176

rl—I—I—l I

JI

a?4'N

.12

10

.8

6

4

.2

.2

1.4

6

8

10

12

larft iS

» X<*# \

<V

)—

1

°i <]—I— I I I

1—I—HH—HH h—

I

1— I'

I I—

h

140 144 148 152 156 160 164 168 172

K'SISO176

Fig. 57. Net contribution of vertical velocity from eightforcing functions after subtracting vorticity ad-vection and Laplacian of thermal advection compo-nents from the total vertical velocity at 700 mbs,00Z 3 March 1965. sinking, neutral.Interval, 10xl0"5 mbs sec - !.

77

/oot^^.

200

300

\

J

*6S

400

.TOO/

GOO

700 "

800

/

V

\

900

1 000 1 —.2 .3 •^ .5*

w- c»s/sci

Fig. 58* Pressure versus vertical velocity (w) at 8°N144°E, OOZ 3 March 1*65.

78

V. CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER STUDY

Several conclusions and recommendations are made based

on the results of the study.

The relation between the calculated geopotential height

fields and the stream fields becomes increasingly degraded

with height, with the resemblance becoming negligible by

200 mbs. It appears that computation of the actual geopoten-

tial height field would be far superior in representative-

ness if this field were to be used in further calculations.

The close correlation of the non-divergent part of the

wind to the actual wind illustrates the validity of current

barotropic progs currently used by the weather bureau in

Hawaii and by ESSA. These progs use just the non-divergent

part of the wind at 500 mbs, from 30°N to 30°S. The non-

divergent winds are obtained from the actual isogons and

isotachs .with calculations leading to 7 f • The resulting

winds are just moved ahead by prognosis. The results ob-

tained by this method, since the non-divergent part of the

wind represents about 90 percent of the actual wind, is

probably better than what can be done by other methods until

more complete information on winds and cloud coverage is

available.

It is felt that the lack of a moisture input consider-

ably degraded the correlations that might be expected be-

tween the vertical velocities and the ITCZ at levels above

900 mbs. Previous studies have shown that the latent heat

term is a considerable contributor to the upward vertical

79

motion, especially in regions of extensive cumulus activity,

such as the ITCZ It is felt that the rising motion centers

would have been more centrally located near the ITCZ's had

the latent heat term been calculated. Further studies

should definitely include this term in the tropics.

Two aids to the few dew point temperatures available

for computing moisture are cloud pictures and the channel

two water vapor data. Areas and types of cloud coverage may

be obtained from cloud pictures and the channel two data is

a good indication as to what level the clouds extend, thus

being able to drop off the moisture content above that level,

Krishnamurti has suggested an exponential decrease in mois-

ture with height and this will be used in future studies as

an alternate method of obtaining moisture. Nephanalyses

appear to be too gross for use in numerical calculations and

this is especially true in the tropics.

An illustration of the difficulties with the nephanal-

yses is the case of 1 March 1965 • Fully 90 percent of the

grid is covered by five-tenths or more clouds. Perhaps a

more reliable interpretation of results can be obtained by

selecting a day when photographs show a better defined,

single ITCZ closer to its mean position for a particular

season.

Terrain effects, although not included in this study,

should be added in any region where significant land eleva-

tions occur. The effect of the high mountainous terrain of

New Guinea could have made a significant difference in the

final analysis.

80

The preliminary results of the vertical variation of

Ui at several points indicate that the tropical atmosphere

may be characterized by large values of vertical motion

near the surface, due to friction, small values at interme-

diate levels with much non-divergent flow and large values

again at some higher level where the effect of a greater

number of closed circulations is realized. The vertical

motions are assumed zero at 100 mbs. This would indicate a

vertical picture of strong inflow into a system near the

surface with weak inflow or perhaps outflow near 700 mbs,

inflow again above that level, and outflow near the top of

the atmosphere. Further investigation into this subject is

recommended.

It should be mentioned that a short range forecast is

being made for this area in the future, utilizing the re-

sults obtained here>

in a primitive equation prediction

model. This is being done in a manner correct for small

Rossby number by Dr. T. N. Krishnamurti

.

Further observational work, both through the use of

conventional data and through the use of satellite cloud

photography and infrared radiometric probes will undoubtedly

provide better grounds for parameterization of the sub-grid

scale phenomenon, and continue to give us a better under-

standing of the tropical atmosphere.

81

VI. BIBLIOGRAPHY

1. Baumliefner, D. P. "The Dynamical Structure of theTropical Atmosphere Based on Experiments with aDiagnostic Numerical Model . " Unpublished Master'sthesis, Department of Meteorology, University ofCalifornia, Los Angeles, 1966. 165 pp.

2. Charney, J. Go "The Use of the Primitive Equationsof Motion in Numerical Weather Prediction,"Tellus, Vol. 7, 1955, PP. 22-26.

3° . "Integrations of the Primitive and BalanceEquations," Proceedings of the InternationalSymposium on Numerical Weather Prediction

, pp. 1 31—152. Tokyo, Japan: The Meteorological Societyof Japan, 1962.

^

'

o "A Note on the Large Scale Motion in theTropics," Journal of Atmospheric Sciences , Vol. 20,1963, pp. 607-609.

5. Hawkins, H. F. , and So L „ Rosenthal. "On the Compu-tation of Stream Functions From the Wind Field,"5^2Jithly_ Weather Review, Vol. 93, No. 4, 1965,pp7~245-252.

6. Krishnamurti, T. N. "Numerical Studies of OrganizedCirculation in Subtropical Latitudes." ScientificReport (CWB IO877), Environmental Science ServicesAdministration, 1966a. 90 pp.

"A Diagnostic Balance Model for Studies ofWeather Systems of Low and High Latitudes (RossbyNumber < 1)," Final Report to AFCRL, Air ForceCambridge Research Laboratories, Bedford, Mass.,1966b. tyl pp.

8« . J. Nogues, and D. P. Baumhefner. "On thePartitioning of the Baroclinic Vertical Motions ina Developing Wave Cyclone," Scientific Report(AFCRL 66-^19), Air Force Cambridge ResearchLaboratories, Bedford, Mass., 1966. 59 PP-

9o Kuo, H. L. "On Formation and Intensification ofTropical Cyclones Through Latent Heat Release byCumulus Convection," Journal of AtmosphericSciences, Vol. 22, 1965. pp. ^0-63.

82

10. Miyakoda, K. "Some Characteristic Features of WinterTime Circulations in the Troposphere and LowerStratosphere," Technical Report No. 14, Universityof Chicago, 1963.

11. Ooyama, K. "A Dynamical Model for the Study of Tropi-cal Cyclone Development." Unpublished ScientificReport, Department of Meteorology and Oceanography,New York University

12. Palmer, C.E. "Tropical Meteorology," Compendium ofMeteorology . American Meteorological Society,Boston, Mass., 1951, pp. 859-917.

13. Panofsky, H. Introduction to Dynamic Meteorology .

Pennsylvania: Pennsylvania State University,1956. 2^3 PP.

Ik. Riehl, H. Tropical Meteorology . New York: The McGrawHill Book Company, 195^. 392 pp.

15. 1 and J. S. Malkus. "On the Heat Balance inthe Equatorial Trough Zone," Geophysica , Vol. 6,

1958, pp. 503-525.

16. Rosenthal, S. L. "Some Attempts to Simulate theDevelopment of Tropical Cyclones by NumericalMethods," Monthly Weather Review , Vol. 92, 1964,pp. 1-21.

17. Roth, H. S., D. W. Rabenhorst, and T. A. Stanbury."Intertropical Convergence Zone Meteorology."Scientific Report (NORD 7386), Bureau of Ordnance,Department of the Navy, 1958.

18. Thompson, P. D. Numerical Weather Analysis and Pre -

diction , New York: The Macmillan Company, I96I

.

19. Wiederanders , C. J. "Analyses of Monthly Mean Re-sultant Winds for Standard Pressure ' Levels Overthe Pacific." Scientific Report (AFCRL 296)Air Force Cambridge Research Laboratories, Bedford,Mass., and Navy Weather Research Facility, Norfolk,Va. , 1961. 83 pp.

20. U.S. Department of Commerce, Environmental ScienceServices Administration. Catalogue of Meteorologi -

cal Satellite Data - Tiros IX Television CloudPhotography . Washington: Government PrintingOffice, 1966.

83

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825 E. Haines St.Philadelphia, Pennsylvania

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3. Prof T. N. Krishnamurti 5Department of Meteorology & OceanographyNaval Postgraduate SchoolMonterey, California 939^0

4. Library 2Naval Postgraduate SchoolMonterey, California 939^0

5. Officer in Charge 1

Naval Weather Research FacilityNaval Air Station, Building R-^-8

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85

UNCLASSIFIEDSecurity Classification

DOCUMENT CONTROL DATA • R&D(Saouiity elmaaitiaatian o/ titla, body of aba tract and indexing annotation mull ba ontarod whan tha orarall raport ia elaaaltlad)

1. ORIGINATING ACTIVITY (Corpormta author)

Naval Postgraduate SchoolMonterey, California

2«. REPORT SECURITY CLASSIFICATION

UNCLASSIFIED2 6 BROUP

3. REPORT TITLE

The Intertropical Convergence Zone and Vertical MotionsUsing a Diagnostic Numerical Model

4. DESCRIPTIVE NOTES (Typa ot raport and inctualra dataa)

5 AUTHOR/JJ (Lmat noma, ttrat natma. initial)

Prokop, Phil G., LCDR, USNMurray, John F. , LT , USN

• REPORT DATE

June 1967

7« TOTAL NO. OF RACKS

86

7b. NO. OR RSRS

20• a. CONTRACT OR (RANT NO.

b. RROJCCT NO.

• «. ORIGINATOR'S REPORT NUMBBRfSj

9b. other REPORT NOfSJ (Any othar numbara that may ba maaifnadthla raport)

10. AVAILABILITY/LIMITATION NOTICES *iCTJOl \y mmmmm

11. SUPPLEMENTARY NOTES 12 SPONSORING MILITARY ACTIVITY

13. ABSTRACT

A diagnostic, non-linear balanced model is applied to a casestudy in the tropical Western Pacific on 1 and 3 March 1965. Theregion includes both sides of the equator and contains the ITCZ

.

A discussion of the ITCZ is given and the model is discussedalong with the processing of the input data. The study containsthe horizontal wind velocity and the thermal distribution as inputvalues. The non-divergent stream function (^ ) is obtained byrelaxation of the Poisson Equation, V z y = IK-7 xV^^ , wherethe vorticity is computed from the observed wind field. A com-parison is made between the non-divergent part of the wind and theactual wind. Computer analyzed stream functions at several levelsare shown and discussed.

Dry adiabatic vertical velocities are obtained and comparedwith the ITCZ. Typical magnitudes are on the order of 0.5 cm/sec.The forcing functions of the *o equation are shown and the contri-butions, in partitioned form, by various terms are illustrated anddiscussed at several levels.

DD FORM 1473 87 UNCLASSIFIEDSecurity Classification

UNCLASSIFIEDSecurity Classification

KEY AO R DS

Intertropical Convergence Zone

Diagnostic

Non-linear

Balanced Model

Non-divergent

Stream function

Partitioned

Vertical motion

. 4

«

*

DD FORMI NOV 651473 ( back ) 88 UNCLASSIFIED

S/N 0101 -807-6821 Security Classification A- 3 1 409

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